Problem: Determine the intercepts of the line. $4x-1=3y+5$ $x$ -intercept: $\Big($
The $x$ -intercept of a graph is the point of intersection between the $x$ -axis and the graph. Since the $x$ -axis is also the line $y=0$, the $y$ -value of this point will always be $0$. The $y$ -intercept of a graph is the point of intersection between the $y$ -axis and the graph. Since the $y$ -axis is also the line $x=0$, the $x$ -value of this point will always be $0$. To find the $x$ -intercept, let's substitute $ y= 0$ into the equation and solve for $x$ : $\begin{aligned}4x-1&=3\cdot{0}+5\\ 4x-1&=5\\ 4x&=6\\ x&=1.5\end{aligned}$ So the $x$ -intercept is $\left(1.5,0\right)$. To find the $y$ -intercept, let's substitute $ x= 0$ into the equation and solve for $y$ : $\begin{aligned}4\cdot0-1&=3y+5\\ -1&=3y+5\\ -6&=3y\\ -2&=y\end{aligned}$ So the $y$ -intercept is $\left(0,-2\right)$. In conclusion, The $x$ -intercept is $\left(1.5,0\right)$. The $y$ -intercept is $\left(0,-2\right)$.